Title: Physics-based control-oriented modeling of the current density profile evolution in NSTX-Upgrade

Active control of the toroidal current density profile is among those plasma control milestones that the National Spherical Torus eXperiment-Upgrade (NSTX-U) program must achieve to realize its next-step operational goals. Motivated by the coupled, nonlinear, multivariable, distributed-parameter plasma dynamics, the first step towards control design is the development of a physics-based, control-oriented model for the current profile evolution in response to non-inductive current drives and heating systems. The evolution of the toroidal current density profile is closely related to the evolution of the poloidal magnetic flux profile, whose dynamics is modeled by a nonlinear partial differential equation (PDE) referred to as the magnetic-flux diffusion equation (MDE). The proposed control-oriented model predicts the spatial-temporal evolution of the current density profile by combining the nonlinear MDE with physics-based correlations obtained at NSTX-U for the electron density, electron temperature, and non-inductive current drives (neutral beams). The resulting first-principles-driven, control-oriented model is tailored for NSTX-U based on predictions by the time-dependent transport code TRANSP. Furthermore, main objectives and possible challenges associated with the use of the developed model for the design of both feedforward and feedback controllers are also discussed.

@article{osti_1465372,
title = {Physics-based control-oriented modeling of the current density profile evolution in NSTX-Upgrade},
author = {Ilhan, Zeki O. and Barton, Justin E. and Schuster, Eugenio and Gates, David A. and Gerhardt, Stefan P. and Menard, Jonathan E.},
abstractNote = {Active control of the toroidal current density profile is among those plasma control milestones that the National Spherical Torus eXperiment-Upgrade (NSTX-U) program must achieve to realize its next-step operational goals. Motivated by the coupled, nonlinear, multivariable, distributed-parameter plasma dynamics, the first step towards control design is the development of a physics-based, control-oriented model for the current profile evolution in response to non-inductive current drives and heating systems. The evolution of the toroidal current density profile is closely related to the evolution of the poloidal magnetic flux profile, whose dynamics is modeled by a nonlinear partial differential equation (PDE) referred to as the magnetic-flux diffusion equation (MDE). The proposed control-oriented model predicts the spatial-temporal evolution of the current density profile by combining the nonlinear MDE with physics-based correlations obtained at NSTX-U for the electron density, electron temperature, and non-inductive current drives (neutral beams). The resulting first-principles-driven, control-oriented model is tailored for NSTX-U based on predictions by the time-dependent transport code TRANSP. Furthermore, main objectives and possible challenges associated with the use of the developed model for the design of both feedforward and feedback controllers are also discussed.},
doi = {10.1016/j.fusengdes.2017.04.028},
journal = {Fusion Engineering and Design},
number = C,
volume = 123,
place = {United States},
year = {2017},
month = {5}
}

DIII-D experimental results are reported to demonstrate the potential of physics-model-based safety factor profile control for robust and reproducible sustainment of advanced scenarios. In the absence of feedback control, variability in wall conditions and plasma impurities, as well as drifts due to external disturbances, can limit the reproducibility of discharges with simple pre-programmed scenario trajectories. The control architecture utilized is a feedforward + feedback scheme where the feedforward commands are computed off-line and the feedback commands are computed on-line. In this work, firstly a first-principles-driven (FPD), physics-based model of the q profile and normalized beta (β N) dynamics is embeddedmore » into a numerical optimization algorithm to design feedforward actuator trajectories that sheer the plasma through the tokamak operating space to reach a desired stationary target state that is characterized by the achieved q profile and β N. Good agreement between experimental results and simulations demonstrates the accuracy of the models employed for physics-model-based control design. Secondly, a feedback algorithm for q profile control is designed following a FPD approach, and the ability of the controller to achieve and maintain a target q profile evolution is tested in DIII-D high confinement (H-mode) experiments. The controller is shown to be able to effectively control the q profile when β N is relatively close to the target, indicating the need for integrated q profile and β N control to further enhance the ability to achieve robust scenario execution. Furthermore, the ability of an integrated q profile + β N feedback controller to track a desired target is demonstrated through simulation.« less

Recent experiments on DIII-D demonstrate the potential of physics-model-based q-profile control to improve reproducibility of plasma discharges. A combined feed forward + feedback control scheme is employed to optimize the current ramp-up phase by consistently achieving target q profiles (Target 1: q min = 1.3,q 95 = 4:4; Target 2: q min = 1.65,q 95 = 5.0; Target 3: q min = 2.1,q 95 = 6:2) at prescribed times during the plasma formation phase (Target 1: t = 1.5 s; Target 2: t = 1:3 s; Target 3: t = 1.0 s). At the core of the control scheme ismore » a nonlinear, first-principles-driven, physics-based, control-oriented model of the plasma dynamics valid for low confinement (L-mode) scenarios. To prevent undesired L-H transitions, a constraint on the maximum allowable total auxiliary power is imposed in addition to the maximum powers for the individual heating and current-drive sources. Experimental results are presented to demonstrate the effectiveness of the combined feed forward + feedback control scheme to consistently achieve the desired target profiles at the predefined times. Here, these results also show how the addition of feedback control significantly improves upon the feed forward only control solution by reducing the matching error and also how the feedback controller is able to reduce the matching error as the constraint on the maximum allowable total auxiliary power is relaxed while keeping the plasma in L-mode.« less

Enabled by the comprehensive measurements from the Magnetic Electron Ion Spectrometer (MagEIS), Helium Oxygen Proton Electron mass spectrometer (HOPE), and Radiation Belt Storm Probes Ion Composition Experiment (RBSPICE) instruments onboard Van Allen Probes in the heart of the radiation belt, the relative contributions of ions with different energies and species to the ring current energy density and their dependence on the phases of geomagnetic storms are quantified. The results show that lower energy (<50 keV) protons enhance much more often and also decay much faster than higher-energy protons. During the storm main phase, ions with energies <50 keV contribute moremore » significantly to the ring current than those with higher energies; while the higher-energy protons dominate during the recovery phase and quiet times. The enhancements of higher-energy proton fluxes as well as energy content generally occur later than those of lower energy protons, which could be due to the inward radial diffusion. For the 29 March 2013 storm we investigated in detail that the contribution from O + is ~25% of the ring current energy content during the main phase and the majority of that comes from <50 keV O +. This indicates that even during moderate geomagnetic storms the ionosphere is still an important contributor to the ring current ions. Using the Dessler-Parker-Sckopke relation, the contributions of ring current particles to the magnetic field depression during this geomagnetic storm are also calculated. In conclusion, the results show that the measured ring current ions contribute about half of the Dst depression.« less

Experimental results from the National Spherical Torus Experiment (NSTX), a medium-size spherical tokamak with a compact divertor, and DIII-D, a large conventional aspect ratio tokamak, demonstrate that the snowflake (SF) divertor configuration may provide a promising solution for mitigating divertor heat loads and target plate erosion compatible with core H-mode confinement in future fusion devices, where the standard radiative divertor solution may be inadequate. In NSTX, where the initial high-power SF experiment were performed, the SF divertor was compatible with H-mode confinement, and led to the destabilization of large ELMs. However, a stable partial detachment of the outer strike pointmore » was also achieved where inter-ELM peak heat flux was reduced by factors 3-5, and peak ELM heat flux was reduced by up to 80% (cf. standard divertor). The DIII-D studies show the SF divertor enables significant power spreading in attached and radiative divertor conditions. Results include: compatibility with the core and pedestal, peak inter-ELM divertor heat flux reduction due to geometry at lower n e, and ELM energy and divertor peak heat flux reduction, especially prominent in radiative D 2-seeded SF divertor, and nearly complete power detachment and broader radiated power distribution in the radiative D 2-seeded SF divertor at P SOL = 3 - 4 MW. A variety of SF configurations can be supported by the divertor coil set in NSTX Upgrade. Edge transport modeling with the multi-fluid edge transport code UEDGE shows that the radiative SF divertor can successfully reduce peak divertor heat flux for the projected P SOL ≃9 MW case. In conclusion, the radiative SF divertor with carbon impurity provides a wider n e operating window, 50% less argon is needed in the impurity-seeded SF configuration to achieve similar q peak reduction factors (cf. standard divertor).« less